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March 2016 Secrecy coverage in two dimensions
Amites Sarkar
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Adv. in Appl. Probab. 48(1): 1-12 (March 2016).

Abstract

Working in the infinite plane R2, consider a Poisson process of black points with intensity 1, and an independent Poisson process of red points with intensity λ. We grow a disc around each black point until it hits the nearest red point, resulting in a random configuration Aλ, which is the union of discs centered at the black points. Next, consider a fixed disc of area n in the plane. What is the probability pλ(n) that this disc is covered by Aλ? We prove that if λ3nlogn = y then, for sufficiently large n, e-8π2ypλ(n) ≤ e-2π2y/3. The proofs reveal a new and surprising phenomenon, namely, that the obstructions to coverage occur on a wide range of scales.

Citation

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Amites Sarkar. "Secrecy coverage in two dimensions." Adv. in Appl. Probab. 48 (1) 1 - 12, March 2016.

Information

Published: March 2016
First available in Project Euclid: 8 March 2016

zbMATH: 1338.60028
MathSciNet: MR3473564

Subjects:
Primary: 60D05
Secondary: 05D40

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 1 • March 2016
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